Use Theorem $0.25$ to derive a formula for calculating the size of the monthly payment for a mortgage in terms of the principal $P,$ the interest rate $I,$ and the number of payments, $t.$ Assume that after $t$ payments have been made, the loan amount is reduced to $0.$ Use the formula to calculate the dollar amount of each monthly payment for a $30-$year mortgage with $360$ monthly payments on an initial loan amount of $\$100,000$ with a $5\%$ annual interest rate.
Hint$:$ Theorem $0.25$ are explained in page number $24 – 25.$
